The rectangle is divided into four parts U, V, W and X. The ratio of Part U to Part V is 7 : 3 and the ratio of Part V to Part W is 3 : 1.
- Find the ratio of Part U to Part V to Part W.
- Given that Part X is 72 m2 , find the area of the rectangle.
(a)
U |
V |
W |
X |
7x1 |
3x1 |
|
|
|
3x1 |
1x1 |
|
7 u |
3 u |
1 u |
72 m2 |
Part V is the repeated identity.
LCM of 3 and 3 = 3
Part U : Part V : Part W = 7 : 3 : 1
(b)
Part U + Part V = Half of the rectangle
Part W + Part X = Half of the rectangle
Part U + Part V and Part W + Part X are equal.
Part U + Part V = Part W + Part X
7 u + 3 u = 1 u + 72
7 u + 3 u - 1 u = 72
9 u = 72
1 u = 72 ÷ 9 = 8
Area of the rectangle
= 2 x (1 u + 72)
= 2 x (1 x 8 + 72)
= 2 x (8 + 72)
= 2 x 80
= 160 m
2 Answer(s): (a) 7 : 3 : 1; (b) 160 m
2